The norm of an averaging operator

Ruud Martini; Gerhard F. Post

The norm of an averaging operator

Ruud Martini
, Gerhard F. Post

Discrete Mathematics and Mathematical Programming

Research output: Book/Report › Report › Professional

114 Downloads (Pure)

Abstract

We consider the operator $A: \ell^2 \to \ell^2$ defined by $A(a) = b$ for $a=(a_n)$ and $b=(b_n)$ with $b_n=\dfrac1n (a_1+a_2+\dots + a_n)$. We prove that $A$ has norm 2.

Original language	English
Place of Publication	Enschede
Publisher	Meetkundig en toegepast-algebraisch onderzoek
Number of pages	4
Publication status	Published - 2001

Publication series

Name	Memorandum / Department of Applied Mathematics
Publisher	University of Twente, Department of Applied Mathematics
No.	1578
ISSN (Print)	0169-2690

Keywords

MSC-47B37
MSC-46B45

Access to Document

ReportFinal published version, 69.9 KB

Cite this

@book{83ee0411dbba499ca9760241eb32f891,

title = "The norm of an averaging operator",

abstract = "We consider the operator \$A: \textbackslash{}ell\textasciicircum{}2 \textbackslash{}to \textbackslash{}ell\textasciicircum{}2\$ defined by \$A(a) = b\$ for \$a=(a\_n)\$ and \$b=(b\_n)\$ with \$b\_n=\textbackslash{}dfrac1n (a\_1+a\_2+\textbackslash{}dots + a\_n)\$. We prove that \$A\$ has norm 2.",

keywords = "MSC-47B37, MSC-46B45",

author = "Ruud Martini and Post, \{Gerhard F.\}",

year = "2001",

language = "English",

series = "Memorandum / Department of Applied Mathematics",

publisher = "Meetkundig en toegepast-algebraisch onderzoek",

number = "1578",

}

TY - BOOK

T1 - The norm of an averaging operator

AU - Martini, Ruud

AU - Post, Gerhard F.

PY - 2001

Y1 - 2001

N2 - We consider the operator $A: \ell^2 \to \ell^2$ defined by $A(a) = b$ for $a=(a_n)$ and $b=(b_n)$ with $b_n=\dfrac1n (a_1+a_2+\dots + a_n)$. We prove that $A$ has norm 2.

AB - We consider the operator $A: \ell^2 \to \ell^2$ defined by $A(a) = b$ for $a=(a_n)$ and $b=(b_n)$ with $b_n=\dfrac1n (a_1+a_2+\dots + a_n)$. We prove that $A$ has norm 2.

KW - MSC-47B37

KW - MSC-46B45

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - The norm of an averaging operator

PB - Meetkundig en toegepast-algebraisch onderzoek

CY - Enschede

ER -